Has any anime been produced that continues the 6 episodes of Golden Boy (Kintaro) or is otherwise inspired by it?
The Golden Boy OVA is only 6 episodes. There hasn't been any more adapted from the manga (which is a lot racier than the anime). The closest thing to a continuation is the recent "Golden Boy 2" manga which is outright pornography.
It's hard to say if there's anything that's inspired by Golden Boy. Tatsuya Egawa, Golden Boy's creator, produced lots of other manga and various degrees of pornographic films which you could say might be inspired by his other creations. Kousuke Fujishima, the creator of "Oh My Goddess", used to work for him as an assistant but I don't know of any interviews or sources indicating that he was inspired by Golden Boy.